@article{CATTANI200782,
    Abstract = {We study the problem of counting the total number of affine solutions of a system of n binomials in n variables over an algebraically closed field of characteristic zero. We show that we may decide in polynomial time if that number is finite. We give a combinatorial formula for computing the total number of affine solutions (with or without multiplicity) from which we deduce that this counting problem is \#P-complete. We discuss special cases in which this formula may be computed in polynomial time; in particular, this is true for generic exponent vectors.},
    Author = {Cattani, Eduardo and Dickenstein, Alicia},
    File = {Counting solutions to binomial complete intersections - 1-s2.0-S0885064X06000240-main - a.pdf},
    ISSN = {0885-064X},
    Journal = {Journal of Complexity},
    Keywords = {Binomial ideal, Complete intersection, -complete},
    Number = {1},
    Pages = {82-107},
    Title = {Counting solutions to binomial complete intersections},
    URL = {https://www.sciencedirect.com/science/article/pii/S0885064X06000240},
    Volume = {23},
    Year = {2007},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0885064X06000240},
    bdsk-url-2 = {https://doi.org/10.1016/j.jco.2006.04.004},
    date-added = {2022-11-26 08:21:18 +0100},
    date-modified = {2022-11-26 08:21:18 +0100},
    doi = {10.1016/j.jco.2006.04.004}
}

@article{CATTANI200782, Abstract = {We study the problem of counting the total number of affine solutions of a system of n binomials in n variables over an algebraically closed field of characteristic zero. We show that we may decide in polynomial time if that number is finite. We give a combinatorial formula for computing the total number of affine solutions (with or without multiplicity) from which we deduce that this counting problem is #P-complete. We discuss special cases in which this formula may be computed in polynomial time; in particular, this is true for generic exponent vectors.}, Author = {Cattani, Eduardo and Dickenstein, Alicia}, File = {Counting solutions to binomial complete intersections - 1-s2.0-S0885064X06000240-main - a.pdf}, ISSN = {0885-064X}, Journal = {Journal of Complexity}, Keywords = {Binomial ideal, Complete intersection, -complete}, Number = {1}, Pages = {82-107}, Title = {Counting solutions to binomial complete intersections}, URL = {https://www.sciencedirect.com/science/article/pii/S0885064X06000240}, Volume = {23}, Year = {2007}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0885064X06000240}, bdsk-url-2 = {https://doi.org/10.1016/j.jco.2006.04.004}, date-added = {2022-11-26 08:21:18 +0100}, date-modified = {2022-11-26 08:21:18 +0100}, doi = {10.1016/j.jco.2006.04.004} }